Jen and Talesha

Mathematics Common Core Standards for Grade 4

• Use the four operations with whole numbers to solve problems
  • Verbally describe and comprehend a multiplication equation.
    • EXAMPLE PRACTICE: The red ribbon is 6 inches long. The blue ribbon is 3 times longer. How long is the blue ribbon?
  • Comprehend and utilize multiplication and division to solve a word problem. (recognize the connections between adding and multiplying)
  • Navigate a multiple step word problems utilizing the 4 operations, interpret remainders and recognize correct answers by rounding, estimating and common sense.
• Gain familiarity with factors and multiples.
  • Work with whole numbers 1-100 in a factoring sense, recognizing its place in the factoring methods and determining prime or composite.

• Generate and analyze patterns.
  • Create patterns by rules. Recognize features that were not specifically identified. Comprehend and verbally describe how the numbers in these patterns change from even to odd and why.

• Generalize place value understanding for multi-digit whole numbers.
  • Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• Use place value understanding to round multi-digit whole numbers to any place.
  • Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays,and/or area models.Multiplication Distributive Split
  • Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models.

• Understand decimal notation for fractions, and compare decimal fractions
  • Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
  • Use decimal notation for fractions with denominators 10 or 100.
  • Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
    Example: For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
    
    
• Extend understanding of fraction equivalence and ordering
  • Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.
  • Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model
• Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers
  • Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
    • a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
    • Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
    • c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
    • d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
  • Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
    • a. Understand a fraction a/b as a multiple of 1/b.
      • For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
    • b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
    • c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
  • Know relative sizes of measurements with units km, m, cm; kg, g; lb, oz; L, ml; hr, min, sec
  • Convert measurements to smaller or larger units; be able to make a conversion chart
  • Using the 4 basic operations solve world problems that involve distance, intervals of time, liquid volumes, masses of objects and money
  • Have the ability to use simple fractions and decimals in problems and convert larger quantities to smaller quantities
  • Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
• Represent and interpret data
  • Make a line plot displaying fractions
  • Solve problems involving addition subtraction of fractions of fractions using a line plot they made
• Understand concepts of angles and have the ability to measure angles (geometric measurement)
  • Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

• Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
• Recognize angle measure as additive. The angle measure of the whole is the sum of the angle measures of the parts.
• Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

• Have the ability to draw and identify lines and angles; Classify shapes by properties of their lines and angles
  • Able to draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular and parallel lines
  • Classify two dimensional figures based on the presence or absence of parallel or perpendicular lines and different angle measurements.
  • Be able to pick out right triangles and recognize them as a category of triangles
  • Know and recognize lines of symmetry in a two-dimensional figure - be able to draw them in on different shapes